// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_PRODUCT_H
#define EIGEN_PRODUCT_H

namespace Eigen {

template <typename Lhs, typename Rhs, int Option, typename StorageKind> class ProductImpl;

namespace internal {

    template <typename Lhs, typename Rhs, int Option> struct traits<Product<Lhs, Rhs, Option>>
    {
        typedef typename remove_all<Lhs>::type LhsCleaned;
        typedef typename remove_all<Rhs>::type RhsCleaned;
        typedef traits<LhsCleaned> LhsTraits;
        typedef traits<RhsCleaned> RhsTraits;

        typedef MatrixXpr XprKind;

        typedef typename ScalarBinaryOpTraits<typename traits<LhsCleaned>::Scalar, typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;
        typedef
            typename product_promote_storage_type<typename LhsTraits::StorageKind, typename RhsTraits::StorageKind, internal::product_type<Lhs, Rhs>::ret>::ret
                StorageKind;
        typedef typename promote_index_type<typename LhsTraits::StorageIndex, typename RhsTraits::StorageIndex>::type StorageIndex;

        enum
        {
            RowsAtCompileTime = LhsTraits::RowsAtCompileTime,
            ColsAtCompileTime = RhsTraits::ColsAtCompileTime,
            MaxRowsAtCompileTime = LhsTraits::MaxRowsAtCompileTime,
            MaxColsAtCompileTime = RhsTraits::MaxColsAtCompileTime,

            // FIXME: only needed by GeneralMatrixMatrixTriangular
            InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(LhsTraits::ColsAtCompileTime, RhsTraits::RowsAtCompileTime),

            // The storage order is somewhat arbitrary here. The correct one will be determined through the evaluator.
            Flags = (MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1) ?
                        RowMajorBit :
                        (MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1) ?
                        0 :
                        (((LhsTraits::Flags & NoPreferredStorageOrderBit) && (RhsTraits::Flags & RowMajorBit)) ||
                         ((RhsTraits::Flags & NoPreferredStorageOrderBit) && (LhsTraits::Flags & RowMajorBit))) ?
                        RowMajorBit :
                        NoPreferredStorageOrderBit
        };
    };

}  // end namespace internal

/** \class Product
  * \ingroup Core_Module
  *
  * \brief Expression of the product of two arbitrary matrices or vectors
  *
  * \tparam _Lhs the type of the left-hand side expression
  * \tparam _Rhs the type of the right-hand side expression
  *
  * This class represents an expression of the product of two arbitrary matrices.
  *
  * The other template parameters are:
  * \tparam Option     can be DefaultProduct, AliasFreeProduct, or LazyProduct
  *
  */
template <typename _Lhs, typename _Rhs, int Option>
class Product : public ProductImpl<_Lhs,
                                   _Rhs,
                                   Option,
                                   typename internal::product_promote_storage_type<typename internal::traits<_Lhs>::StorageKind,
                                                                                   typename internal::traits<_Rhs>::StorageKind,
                                                                                   internal::product_type<_Lhs, _Rhs>::ret>::ret>
{
public:
    typedef _Lhs Lhs;
    typedef _Rhs Rhs;

    typedef typename ProductImpl<Lhs,
                                 Rhs,
                                 Option,
                                 typename internal::product_promote_storage_type<typename internal::traits<Lhs>::StorageKind,
                                                                                 typename internal::traits<Rhs>::StorageKind,
                                                                                 internal::product_type<Lhs, Rhs>::ret>::ret>::Base Base;
    EIGEN_GENERIC_PUBLIC_INTERFACE(Product)

    typedef typename internal::ref_selector<Lhs>::type LhsNested;
    typedef typename internal::ref_selector<Rhs>::type RhsNested;
    typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
    typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;

    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Product(const Lhs& lhs, const Rhs& rhs) : m_lhs(lhs), m_rhs(rhs)
    {
        eigen_assert(lhs.cols() == rhs.rows() && "invalid matrix product" &&
                     "if you wanted a coeff-wise or a dot product use the respective explicit functions");
    }

    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }

    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const LhsNestedCleaned& lhs() const { return m_lhs; }
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const RhsNestedCleaned& rhs() const { return m_rhs; }

protected:
    LhsNested m_lhs;
    RhsNested m_rhs;
};

namespace internal {

    template <typename Lhs, typename Rhs, int Option, int ProductTag = internal::product_type<Lhs, Rhs>::ret>
    class dense_product_base : public internal::dense_xpr_base<Product<Lhs, Rhs, Option>>::type
    {
    };

    /** Conversion to scalar for inner-products */
    template <typename Lhs, typename Rhs, int Option>
    class dense_product_base<Lhs, Rhs, Option, InnerProduct> : public internal::dense_xpr_base<Product<Lhs, Rhs, Option>>::type
    {
        typedef Product<Lhs, Rhs, Option> ProductXpr;
        typedef typename internal::dense_xpr_base<ProductXpr>::type Base;

    public:
        using Base::derived;
        typedef typename Base::Scalar Scalar;

        EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE operator const Scalar() const { return internal::evaluator<ProductXpr>(derived()).coeff(0, 0); }
    };

}  // namespace internal

// Generic API dispatcher
template <typename Lhs, typename Rhs, int Option, typename StorageKind>
class ProductImpl : public internal::generic_xpr_base<Product<Lhs, Rhs, Option>, MatrixXpr, StorageKind>::type
{
public:
    typedef typename internal::generic_xpr_base<Product<Lhs, Rhs, Option>, MatrixXpr, StorageKind>::type Base;
};

template <typename Lhs, typename Rhs, int Option> class ProductImpl<Lhs, Rhs, Option, Dense> : public internal::dense_product_base<Lhs, Rhs, Option>
{
    typedef Product<Lhs, Rhs, Option> Derived;

public:
    typedef typename internal::dense_product_base<Lhs, Rhs, Option> Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
protected:
    enum
    {
        IsOneByOne = (RowsAtCompileTime == 1 || RowsAtCompileTime == Dynamic) && (ColsAtCompileTime == 1 || ColsAtCompileTime == Dynamic),
        EnableCoeff = IsOneByOne || Option == LazyProduct
    };

public:
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index row, Index col) const
    {
        EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
        eigen_assert((Option == LazyProduct) || (this->rows() == 1 && this->cols() == 1));

        return internal::evaluator<Derived>(derived()).coeff(row, col);
    }

    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index i) const
    {
        EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
        eigen_assert((Option == LazyProduct) || (this->rows() == 1 && this->cols() == 1));

        return internal::evaluator<Derived>(derived()).coeff(i);
    }
};

}  // end namespace Eigen

#endif  // EIGEN_PRODUCT_H
